We introduce an axiomatic definition of a conditional convex risk mapping. By employing the techniques of conjugate duality we derive properties of conditional risk mappings. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We...

In this paper we consider a new class of continuous location problems where the “distances” are measured by gauges of closed (not necessarily bounded) convex sets. These distance functions do not satisfy the definiteness property and therefore they can be used to model those situations where...

In a series of papers, Hiriart-Urruty proposed necessary and sufficient global optimality conditions for the so-called d.c. problem and the convex maximization problem. In this paper, we investigate the underlying local optimality conditions, which, in general, are necessary, but not sufficient...

In this paper we consider a new class of continuous location problems where the “distances” are measured by gauges of closed (not necessarily bounded) convex sets. These distance functions do not satisfy the definiteness property and therefore they can be used to model those situations where...

In a series of papers, Hiriart-Urruty proposed necessary and sufficient global optimality conditions for the so-called d.c. problem and the convex maximization problem. In this paper, we investigate the underlying local optimality conditions, which, in general, are necessary, but not sufficient...

This article is devoted to adverse selection problems in which individual private information is a whole utility function and cannot be reduced to some finite-dimensional parameter. In this case, incentive-compatibility conditions can be conveniently expressed using some abstract convexity...

We introducea new computational framework for DEA that reduces computationtimes and increases flexibility in applications over multiplemodels and orientations.The process is based on the identificationof frames--minimal subsets of the data needed to describethe models in the problems--for each...